Improved bound for quantum-speed-limit time in open quantum systems by introducing an alternative fidelity

In this paper, we introduce an alternative quantum fidelity for quantum states which perfectly satisfies all of Jozsa's axioms and is zero for orthogonal states. By employing this fidelity, we derive an improved bound for quantum-speed-limit time in open quantum systems in which the initial states can be chosen as either pure or mixed. This bound leads to the well-known Mandelstamm-Tamm-type bound for nonunitary dynamics in the case of initial pure states. However, in the case of initial mixed states, the bound provided by the introduced fidelity is tighter and sharper than the obtained bounds in the previous works.